Sampled-data H ∞ control for a class of Markovian jump systems with input saturation via stochastic sampling design

This paper deals with the problem of H ∞ control for a stochastic sampling Markovian jump system subject to input saturation. The stochastic sampling we address is a Bernoulli distribution and two different sampling periods are considered whose occurrence probabilities are known constants. Actually the control method in this paper can be applied to a system with multiple stochastic sampling periods. By transforming the original stochastic sampling Markovian jump system into a continuous Markovian jump delayed systems, the plant can be stabilized by a state-feedback controller with input saturation. By applying an appropriate Lyapunov–Krasovskii function, some sufficient conditions for the stabilization of the system and the H ∞ controller design are derived in terms of linear matrix inequalities. Finally, in order to validate the efficiency of the approach mentioned above, a simulation example is provided.

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